I think she was probably spouting rubbish... Menagerie brought the events and characters of The Cage into canon, and Pike's XO seemed, for all intents and purposes, to be rather formidable. Given the ostensible reverence TOS had for starship commanders, I can't see Starfleet denying a command to somebody with her level of training and experience based on anatomy alone.
True but some might argue canon was about as consistent as laughing Vulcans. It was the network execs that did not take to the Number one character so her nonsmiling, expressionless personality was transferred to Spock. As for 'The Cage' it had no concept of a galactic Federation. The set up was based on an Earth/Human only space program.
Come to think of it in TNG when the Enterpise came across Federation colonies they were dominated or 100 per cent populated by humans of European descent, in fifteen years of space travel that is ridiculous.